11 PM EST

SECTION 1

A. Journal Week 2

Chapter 4 in Affirming Diversity pages 65-91.

1. How might you make a convincing argument that all students should have equal access and opportunity to algebra or its integrated counterpart in grade 8 and advanced placement courses in high school?

Reflect upon the following curriculum questions:

· In what ways is the mathematics curriculum limiting or detrimental?

· In what ways is the mathematics curriculum beneficial?

· Does the classroom teacher make his/her own mathematics curriculum and if so how is it evaluated in terms of student achievement?

· Have you and/or your colleagues been involved in developing the curriculum or do you rely on the textbooks?

Reflect upon the following pedagogy questions:

· What might you look for in order to identify the philosophical framework of a practitioner's pedagogy?

· How can pedagogical strategies reflect or promote anti-bias, equity, or social justice?

· What do you need to know in order to identify and claim your own pedagogy?

Read the Case Study: Linda Howard. Chapter 4, pages 91-101.

Answer the following questions in your journals:

1. If you were one of Linda's teachers, how might you show her that you affirm her identity? Provide specific examples.

2. What kind of teachers have most impressed Linda? Why? What can you learn from this in our own teaching?

3. What skills do you think teachers need if they are to face the concerns of race and identity effectively?

B. Journal Week 3—ANSWER QUESTIONS & REFLECT

A group of students were asked to compare the following ratios which represent the amount of orange concentrate mixed with the amount of water. The students needed to determine which of the mixes was the most 'orangey." The students were also told they could not convert the ratios to decimals or percents, nor could they use calculators.

		Orange Mix		Water
a.		1	to	3
b.		2	to	5
c.		3	to	7
d.		4	to	11

One student responded as follows:   What does the evidence in this work tell you about the student's understanding of comparing ratios? How would you respond to the student?

C. Journal week 7---REFLECTION ON ARTICLE

D. JOURNAL WEEK 8

"Each student, regardless of disability, difference, or diversity, needs access to the curriculum that is meaningful and that allows the student to use his or her strengths."

Earlier in this course we examined templates for multiple representations and for vocabulary development. Examine the following graphic organizer: From Math for All: Differentiation Instruction, Grades 3 - 5, pg. 143. Complete this graphic organizer or one of your choosing for the Speeding Ticket problem. How do you think using a graphic organizer will help your students? Would you require all students to use a graphic organizer or only certain students? Explain your thinking.

SECTION 2

A. REPLIES

ELIZABETH: You cannot take a smaller number from a larger number.

I’m thinking this must be a typo.  It should read you couldn’t take a larger number from a smaller number.  This is of course not true.  A number line that goes beyond zero into the negative numbers would illustrate that.  When you multiply the number gets bigger and when you divide the number gets smaller.

This might work for whole numbers, but not a general rule for all.  Fractions and decimals yield a smaller product.  Multiplying is repeated addition of equal groups and division is taking the whole amount and grouping it into equal groups.

Two negatives make a positive.

Also not a good general rule as it only applies to multiplication.  Adding and subtracting integers is always more tricky for my students.  I have a large number line on the floor and students practice walking the line.

Always reduce fractions to lowest terms.

Students must be given clear explanations of lowest terms and simplest form and they need to know if a fraction is in simplest form or not and how to tell.  It is good practice to reduce, but “always” not so.  Students should be able to solve a problem involving fractions and keep the fraction in the terms that relate to the context of the problem.  If the problem is asking how many eighths for instance, their answer shouldn’t be ½, but 4/8. 

Always change an improper fraction to a mixed number.

Again, the “always” is misleading.  Students should be guided when to change to a mixed number and when to keep it as an improper fraction. 

When solving a proportion cross-‐multiply first.

Students may be able to learn the rule, but not understand the problem.  They also will need to be able to correctly align the proportions with the same units as numerators, etc.  Some students may be able to solve the problem by making a table instead; this might make more visual sense to them. 

To multiply mixed numbers always convert them to improper fractions first.

Is this a bad idea?  I tried several ways of multiplying mixed numbers and the only way I could get the correct answer was to convert first.  Maybe if the mixed number isn’t in simplest form?

To multiply binomials always use FOIL.

Wouldn’t this depend on the equation?  If it is just binomials using FOIL makes sense.  But as the equations become more complex, other steps may need to be completed first.  Again, the use of “always” may not lead students in the right direction.

When solving an equation first, always bring the variable to one side of the equation.

This is not the best short cut, as sometimes the variable doesn’t move at all.  Students will need to given clear explanations about isolating the variable. 

Always do the operation inside the parenthesis first.

What about if there isn’t an operation in the parenthesis, they are used for a different purpose or if a fraction is being raised to a power? Also, in algebra, sometimes we can isolate a variable by dividing by the entire parenthesis unit and not solving it first. 

When adding numbers always line up the digits starting at the right.

Students should line up their numbers according to place value, not so they are aligned to the right.  This would then solve problems with decimal addition. 

B. REPLIES APPLICATIONS

KRISTEN

Problem: 3 more than 5 times 6

Correct Solution: 3+ (5x6) = 33

My students would not be able to solve the “3 more than 5 times 6” problem since they don't know how to multiply. However, I would imagine that 3rd graders, or even fourth graders, would work left to right using the rules of literacy. They would assume the problem means “3 more than 5” and then multiply that by “6”. Therefore, they would solve 8 x 6 = 48. Like student A. Students B , C, and D didn’t understand what to multiply and what to add. Student D, however, did try to group part of the problem using parentheses. I would argue that student A’s answer would be the most correct since the work showed technically matches the written word. To address issues, I would want to first sit with each student to hear his/her thinking. Then, I would possibly try the following suggestions.

One way to modify the problem would be to provide it in numeric form, not written in words or spoken orally where there could be a misunderstanding. Instead, I would show 3 + (5 x 6) = ?. Now, students can understand what is being done. Or, I could break the problem down into steps 1. Five times six. 2. Three more than five times six.

The number of speeding tickets in Quincy have dropped from 210 tickets in October to 190 tickets in November. What is the percent of decrease?

a. 5% - I am not sure where this error comes from.

b. 10% - This error probably stems from the fact that the student knows that that there are 20 less tickets, and they probably calculated 20 tickets/190 tickets is about 10.5% decrease.

c. 20%- This error may stem from the fact that there were 20 less tickets given so the student assumed it meant a 20% decrease.

d. 90% - This error probably stems from the fact that the student figured out that 190 tickets is 90% of 210 tickets. They may not have understood the calculations they made.






I think students need to have a clearer picture of what is happening. Perhaps I would scale the numbers back to 21 tickets and 19 tickets to make it easier to model. We could use manipulatives. I would also want to revisit how to solve percents and percent decreases. I think my exact strategies would truly depend on which students I was addressing in my small group and how they got to their answer in the first place since I only made guesses on what would have led to the common misconceptions.

SECTION 3

Blog Post

Reflect on your growth and understanding of Data Analysis and Statistics at this point in the course. What has been new for you? What connections can you make to previous knowledge? What themes are emerging in the course? How are concepts connected to each other? to other areas of mathematics and the world around us? What growth do you see in your own mathematical thinking? What connections do you see to your teaching practice? What questions have are you still pondering?

Compose a blog entry of at least 500 words. This piece should be more formal than a weekly reflection, with clear connections to the content of Data Analysis & Statistics. It should be specific to your perspectives in the course - your growth, your questions, big ideas and connections you see. It is a synthesis of your experiences in the past six weeks of the course, with an emphasis on your work in Weeks 3 - 6.

RUBRIC

POSSIBLE DETAILS TO USE FOR THE BLOG ARE ATTACHED